5.6: Methods of Truss Analysis

Introduction

• Two common methods of truss analysis:
  • Method of Joint
  • Method of Section (or Moment)

5.6.1 Sign Convention

• Negative member axial force: Member or joints at both ends are in compression.
• Positive member axial force: Member or joints at both ends are in tension.

5.6.2 Analysis of Trusses by Method of Joint

• Principle: A system in equilibrium allows for joints to be isolated and analyzed.
• Procedure:
  1. Verify truss stability and determinacy.
  2. Determine support reactions.
  3. Identify zero-force members to reduce computations.
  4. Select a joint with ≤2 unknown forces.
  5. Draw free-body diagram, assume tensile axial forces.
  6. Apply equations (\Sigma F_{X}=0) and (\Sigma F_{Y}=0).
  7. Proceed to next joint with ≤2 unknown forces.
• Example Analysis:
  • Example provided for joints A, B, and D.

5.6.3 Zero Force Members

• Identification:
  1. Noncollinearity at a force-free joint indicates zero-force members.
  2. At a joint with 3 members, if 2 are collinear, the third is a zero-force member.
  3. At a joint, a force parallel to one member and perpendicular to another makes the perpendicular one a zero-force member.

5.6.4 Analysis of Trusses by Method of Section

• Useful for determining axial forces in specific members of large systems.
• Procedure:
  1. Check truss stability and determinacy.
  2. Determine support reactions.
  3. Make an imaginary cut to include desired members.
  4. Apply equilibrium forces to truss parts.
  5. Select a part for force determination.
  6. Use equilibrium conditions.
• Example Analysis:
  • Demonstrated with members CD, CG, and HG.

Chapter Summary

• Internal forces in plane trusses:
  • Trusses: Straight, slender members connected by frictionless pins, subjected to axial forces.
  • Loads applied only at joints.
  • Axial compression is negative; axial tension is positive.
  • Trusses: Externally/Internal determinate or indeterminate.
• Truss Stability and Determinacy:
  • Formulas:
    • (m+r<2j): Unstable
    • (m+r=2j): Determinate
    • (m+r>2j): Indeterminate
• Methods:
  • Method of Joint: Isolates joints, considers equilibrium.
  • Method of Section: Divides truss, considers equilibrium of parts.

Practice Problems

• Problem sets for classification and force determination using both methods.